Name: signal transformations in time and amplitude
Uploaded: 2024-09-26T13:16:54.000Z
Duration: 1 min 22 s
Channel: JoVE

As operações básicas de sinal são reversão de tempo, escala, deslocamento e transformações de amplitude.
A reversão do tempo espelha um sinal de tempo contínuo sobre o eixo vertical no tempo igual a zero, obtido substituindo 't' por 't' negativo. Para um sinal considerado, os resultados são mostrados graficamente.
A escala de tempo comprime ou expande um sinal no tempo, substituindo 't' por 'at', onde 'a' é constante. Se a magnitude dessa constante for maior que 1, o sinal se comprime; se for menor que 1, ele se expande.
Um valor negativo dessa constante induz tanto a reversão do tempo quanto a compressão ou expansão. Isso pode ser representado graficamente usando o sinal considerado.
A mudança de tempo de um sinal de tempo contínuo é feita substituindo 't' por 't − t0', onde 't0' é constante. Uma constante positiva atrasa e desloca o sinal desde a origem, enquanto uma negativa avança o sinal e o desloca para a esquerda.
As transformações de amplitude de um sinal de tempo contínuo assumem a forma geral onde 'A' e 'B' são constantes. O gráfico mostra uma transformação de amplitude de um sinal exemplificado.

operações básicas em sinais

Basic Operations on Signals

As operações básicas de sinais incluem reversão de tempo, escala de tempo, deslocamento de tempo e transformações de amplitude. Essas operações são fundamentais no processamento e análise de sinais.
A reversão de tempo espelha um sinal de tempo contínuo sobre o eixo vertical em t=0. Isso é obtido substituindo t por −t. Por exemplo, se um sinal x(t) for considerado, o sinal reverso no tempo será x(−t). Essa operação pode ser representada graficamente, mostrando o sinal espelhado.
<img alt="Figure1" src="/files/ftp_upload/16044/16044_PT%20Figure_1.svg" style="text-align: center; height: 150px;">
A escala de tempo comprime ou expande um sinal no tempo substituindo t por at, onde a é uma constante. Se ∣a∣&gt;1, o sinal comprime; se ∣a∣&lt;1, ele se expande. Um valor negativo de a induz tanto a reversão do tempo quanto a compressão ou expansão. Uma representação gráfica dessa operação em um sinal demonstra esses efeitos.

A mudança de tempo de um sinal de tempo contínuo é feita substituindo t por t−t_0, onde t_0 é uma constante. Um t_0 positivo atrasa e desloca o sinal para a direita, enquanto um t_0 negativo avança o sinal e o desloca para a esquerda. Por exemplo, um sinal x(t) deslocado por t_0 é representado como x(t−t_0).
Transformações de amplitude de um sinal de tempo contínuo são geralmente da forma Ax(t)+B, onde A e B são constantes. Essas transformações escalam a amplitude e também podem deslocá-la verticalmente. Graficamente, uma transformação de amplitude de um sinal mostra o efeito de escalar por A e deslocar por B.
Essas operações básicas — reversão de tempo, escala, deslocamento e transformações de amplitude — são ferramentas essenciais para manipular e analisar sinais, permitindo vários ajustes e modificações em aplicações de processamento de sinais.

Operações básicas em sinais

As operações básicas de sinal são reversão de tempo, escala, deslocamento e transformações de amplitude.
A reversão do tempo espelha um sinal de tempo contínuo sobre o ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Introduction to Signals and Systems

Introdução a Sinais e Sistemas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

signal transformations in time and amplitude

Signal transformations in time and amplitude are key tools in signal processing. They include time reversal, time scaling, time shifting, and amplitude changes. These operations help students describe how a continuous-time signal changes when it is mirrored, stretched, moved, or resized.

Time reversal flips a continuous-time signal about the vertical axis at t = 0. It is done by replacing t with -t, so x(t) becomes x(-t). A graph of the signal shows this mirrored shape clearly.

Time scaling changes how fast or slow a signal appears in time by replacing t with at, where a is a constant. If |a| &gt; 1, the signal compresses. If |a| &lt; 1, the signal expands. A negative value of a causes time reversal as well as compression or expansion.

Time shifting moves a continuous-time signal left or right by replacing t with t - t0, where t0 is a constant. A positive t0 delays the signal and shifts it to the right. A negative t0 advances the signal and shifts it to the left. Amplitude transformations use the form Ax(t) + B, where A and B are constants. These changes scale the signal’s height and can shift it up or down vertically.

Signal Transformations in Time and Amplitude

signal-transformations-in-time-and-amplitude

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exponential and sinusoidal signals

Complex Exponentials in Signal Behavior

Exponential and sinusoidal signals are used to describe how waveforms change over time. The continuous-time exponential function uses constants α and A. When both are real, it shows exponential growth or decay. Graphs of these signals make the rise or drop easy to see. When α is purely imaginary, the signal becomes a complex exponential. In this form, j is the imaginary unit and ω0 is the angular frequency. A complex exponential is periodic when its magnitude is unity. That periodic behavior...

basic discrete time signals

Discrete-Time Signal Basics and Shapes

Discrete-time signals include several basic sequences used in signal processing. The unit step sequence is 1 for zero and positive values of the integer n. A graph of eight sample points shows it as a step that begins at n = 0 and stays constant after that. The unit impulse, also called the sample sequence, is 0 for every n except at n = 0, where it equals 1. This sequence is written as δ(n). It is the first difference of the unit step sequence, and the unit step sequence u(n) is the...

basic operations on signals

Signal transformations in time and amplitude are key tools in signal processing. They include time reversal, time scaling, time shifting, and amplitude changes. These operations help students describe how a continuous-time signal changes when it is mirrored, stretched, moved, or resized. Time reversal flips a continuous-time signal about the vertical axis at t = 0. It is done by replacing t with -t, so x(t) becomes x(-t). A graph of the signal shows this mirrored shape clearly. Time scaling...

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JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Signal Transformations in Time and Amplitude

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